Work and Energy

Definition of Work

Work is a measure of energy transfer that occurs when an object is moved by a force. It is defined mathematically as:

• Work (W): The product of force and displacement in the direction of the force.

• Formula:

• Units: Joules (J)

• Example: Lifting a box vertically involves work equal to the weight of the box times the height lifted.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion.

• Kinetic Energy (KE):

• Units: Joules (J)

• Example: A moving car has kinetic energy proportional to its mass and the square of its speed.

Potential Energy

Potential energy is stored energy due to an object's position or configuration.

• Gravitational Potential Energy (PE):

• Units: Joules (J)

• Example: A rock at the top of a hill has gravitational potential energy.

Conservation of Energy

Principle of Conservation

The total energy in a closed system remains constant; energy can be transformed from one form to another but cannot be created or destroyed.

• Mechanical Energy: Sum of kinetic and potential energy.

• Conservation Equation:

• Example: A pendulum swings, converting potential energy to kinetic energy and back.

Heat Transfer and Internal Energy

Heat Transfer

Heat is the transfer of thermal energy between systems due to temperature difference.

• Methods: Conduction, convection, and radiation.

• Formula for Heat:

• Units: Joules (J)

• Example: Heating water in a kettle involves heat transfer from the heating element to the water.

Internal Energy

Internal energy is the total energy contained within a system, including kinetic and potential energies of particles.

• Change in Internal Energy:

• First Law of Thermodynamics: Energy added as heat increases internal energy or does work.

• Example: Compressing a gas increases its internal energy.

Momentum and Conservation of Momentum

Momentum

Momentum is the product of an object's mass and velocity, representing the quantity of motion.

• Momentum (p):

• Units: kg·m/s

• Example: A moving truck has more momentum than a moving bicycle at the same speed.

Impulse

Impulse is the change in momentum resulting from a force applied over a time interval.

• Impulse (J):

• Units: kg·m/s or N·s

• Example: Kicking a soccer ball applies an impulse, changing its momentum.

Conservation of Momentum

In a closed system, the total momentum before and after a collision remains constant.

• Conservation Equation:

• Types of Collisions: Elastic (kinetic energy conserved), inelastic (kinetic energy not conserved).

• Example: Two ice skaters push off each other and move in opposite directions, conserving momentum.

Rotational Motion (Maybe Included)

Rotational Kinematics

Rotational motion describes the movement of objects around a fixed axis.

• Angular Displacement (θ): Measured in radians.

• Angular Velocity (ω):

• Angular Acceleration (α):

• Example: A spinning wheel has angular velocity and acceleration.

Rotational Energy

Rotational kinetic energy is the energy due to rotation.

• Formula:

• Moment of Inertia (I): Depends on mass distribution relative to axis.

• Example: A figure skater spinning faster by pulling arms in reduces moment of inertia and increases angular velocity.

Conservation of Angular Momentum

Angular momentum is conserved in a closed system unless acted upon by external torque.

• Angular Momentum (L):

• Conservation Equation:

• Example: A planet orbiting the sun conserves angular momentum.

Additional info: Academic context and formulas have been expanded for completeness. Topics are grouped according to chapters 6-9 as indicated in the materials.